Arfa: An Agile Regime-Based Floating-Point Optimization Approach for Rounding Errors
We introduce a floating-point (FP) error optimization approach called \textsc{Arfa} that partitions the domain $\mathcal{D}$ of an FP expression $f_e$ into \emph{regimes} and rewrites $f_e$ in each regime where $f_e$ shows larger errors. First, \textsc{Arfa} seeks a rewrite substitution $f_o$ with lower errors across $\mathcal{D}$, whose error distribution is plotted for effective regime inference. Next, \textsc{Arfa} generates an incomplete set of ordered rewrite candidates within each regime of interest, so that searching for the best rewrite substitutions is performed efficiently. Finally, \textsc{Arfa} selects the best rewrite substitution by inspecting the errors of top ranked rewrite candidates, with enhancing precision also considered. Experiments on 56 FPbench examples and four real-life programs show that \textsc{Arfa} not only reduces the maximum and average errors of $f_e$ by 4.73 and 2.08 bits on average (and up to 33 and 16 bits), but also exhibits lower errors, sometimes to a significant degree, than Herbie and NumOpt.
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16:10 20mTalk | Arfa: An Agile Regime-Based Floating-Point Optimization Approach for Rounding Errors Technical Papers Jinchen Xu Information Engineering University, Mengqi Cui Information Engineering University, Fei Li Information Engineering University, Zuoyan Zhang Hunan University, Hongru Yang Information Engineering University, Bei Zhou Information Engineering University, Jie Zhao Hunan University DOI | ||
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